---
id: 5900f3b01000cf542c50fec2
title: '問題 67: 経路の最大和 (2)'
challengeType: 1
forumTopicId: 302179
dashedName: problem-67-maximum-path-sum-ii
---

# --description--

下の三角形の頂点から開始し、下の段にある隣接する数字へと移動していくと、頂点から一番下までの最大和は 23 になります。

<div style='text-align: center;'>
  <strong style='color: red;'>3</strong><br>
  <strong style='color: red;'>7</strong> 4<br>
  2 <strong style='color: red;'>4</strong> 6<br>
  8 5 <strong style='color: red;'>9</strong> 3
</div>

すなわち、3 + 7 + 4 + 9 = 23 です。

あらかじめ用意された二次元配列 `numTriangle` に、100 段の三角形が含まれています。この三角形の頂点から一番下までの経路の最大和を求めなさい。

**注:** これは、問題 18 をかなり難しくした問題です。 全部で 2<sup>99</sup> 通りもあるので、すべての経路を試してこの問題を解くことは不可能です！ 毎秒 1 兆 (10<sup>12</sup>) 本の経路を調べることができたとしても、全部を調べるのに 200 億年以上かかるでしょう。 この問題を解くための効率的なアルゴリズムがあります。 ;o)

# --hints--

`maximumPathSumII([[3, 0, 0, 0],[7, 4, 0, 0],[2, 4, 6, 0],[8, 5, 9, 3]])` は数値を返す必要があります。

```js
assert(typeof maximumPathSumII(_testTriangle) === 'number');
```

`maximumPathSumII([[3, 0, 0, 0],[7, 4, 0, 0],[2, 4, 6, 0],[8, 5, 9, 3]])` は 23 を返す必要があります。

```js
assert.strictEqual(maximumPathSumII(_testTriangle), 23);
```

`maximumPathSumII(numTriangle)` は 7273 を返す必要があります。

```js
assert.strictEqual(maximumPathSumII(_numTriangle), 7273);
```

# --seed--

## --before-user-code--

```js
const _testTriangle = [[3, 0, 0, 0],
                      [7, 4, 0, 0],
                      [2, 4, 6, 0],
                      [8, 5, 9, 3]];
const _numTriangle = 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```

## --seed-contents--

```js
function maximumPathSumII(triangle) {

  return true;
}
```

# --solutions--

```js
function maximumPathSumII(triangle) {
  const newTriangle = [];
  for (let i = 0; i < triangle.length; i++) {
    newTriangle.push(triangle[i].slice());
  }

  for (let i = newTriangle.length - 2; i >= 0; i--) {
    for (let j = i; j >= 0; j--) {
      let higherOption = 0;
      if (newTriangle[i + 1][j + 1] > newTriangle[i + 1][j]) {
        higherOption = newTriangle[i + 1][j + 1];
      } else {
        higherOption = newTriangle[i + 1][j];
      }
      newTriangle[i][j] += higherOption;
    }
  }
  return newTriangle[0][0];
}
```
